Disturbance rejection control method For permanent magnet synchronous motor speed-regulation system Shihua Li , Cunjian Xia, Xuan Zhou Elsevier, Mechatronics 22 (2012) 706–714 Advanced Servo Control 12/24/2014 Student: T A R Y U D I / 林運昇 Advisor: Prof. Ming-Shyan Wang

Outline Introduction The mathematical model of PMSM Controller design Speed controller design Current controller design Simulation and experiment results Experimental results Conclusion 2017/4/27

Introduction For the speed loop, regarding parameter variations and load torque as the lumped disturbances, an ESO based disturbance rejection control law is developed. Considering the dynamics of q-axis current, the coupling between rotor speed and d-axis current as well as the back electromotive force are regarded as lumped disturbances for the q-axis current loop, lumped disturbances are estimated by introducing an ESO. Thus a composite control law consisting of proportional feedback and disturbance feedback compensation simplified model is developed to control the q-axis current. 2017/4/27

Introduction The general structure of the PMSM servo system Fig.  The principle block diagram of PMSM system based on vector control. 2017/4/27

The Mathematical Model of PMSM Where:   Rs  : Stator resistance,  ud, uq  : d- and q-axes stator voltages,  id, iq  : d- and q-axes stator currents,  Ld, Lq : d- and q-axes stator inductances, and Ld = Lq = L   np  : Number of pole pairs of the PMSM,  ω  : Rotor angular velocity of the motor,  ψf  : Flux linkage,  TL  : Load torque,  B  : Viscous friction coefficient and  J  : Rotor inertia. 2017/4/27

Controller Design ESO is the main disturbance estimation technique. It regards the lumped disturbances of system, which consists of internal dynamics and external disturbances, as a new state of system The control scheme includes a speed loop and two current loops Fig. The principle diagram of PMSM system under ESO based composite control methods. 2017/4/27

The principle of ESO-based control method Example , how to construct linear ESO will be shown below Where   f ( x, t) : the unknown nonlinear function  d(t) : the external disturbance  u : the control signal x : the output of system   b   : the control gain a  (t  ) = f  (x  , t  ) + d  (t  ) 2017/4/27

Speed controller design Define  x 1 = x  , x 2 = a (t). And a linear ESO can be constructed as follows [1]: Where where −p(p > 0) is the desired double pole of ESO. z1 is the estimate of x1 and z2 is the estimate of a(t). Here, according to the analysis in [1], z1(t) is an estimate of the output x(t) while z2(t) is an estimate of the lumped disturbance a(t), i.e., z1(t) → y(t) and z2(t) → a(t). A composite control law is designed as follows: where x∗ is the reference input of x. 2017/4/27

Speed controller design The torque equation of PMSM system is where Control gain The lumped disturbances consisting of the friction, the external load disturbances, and the tracking error of current-loop of iq 2017/4/27

Speed controller design Then an ESO can be designed as where z1 is the estimate of angular velocity ω, z2 is the estimate of the lumped disturbances. A composite control law of speed loop can be designed as where k   is the proportional gain, ω∗ is the reference speed is the output of speed loop controller 2017/4/27

ESO-based speed controller Fig. 2. The block diagram of ESO-based speed controller 2017/4/27

Current controller design An ESO-based controller is designed for the q-axis current loop. For the d-axis current loop, a standard PI control algorithm is employed. The equation of q  -axis current loop is written as follows: where the lumped disturbances of q  -axis current loop are consisting of the coupling between rotor speed and d-axis current, the dynamics of q-axis current, the back electromotive force The ESO of q-axis current loop can be designed as follows: where −pq(pq > 0) is the desired double pole, z11 is the estimate of iq, and z12 is the estimate of aq(t). 2017/4/27

Current controller design A composite control law of q  -axis current loop can be designed as where k  q is the proportional gain of q  -axis current loop controller  is the q-axis reference current 2017/4/27

PMSM system under ESO based composite control methods A control scheme which employs disturbance rejection control laws for not only speed loop but also the q-axis current loop Fig. 3. The principle diagram of PMSM system under ESO based composite control methods. 2017/4/27

Simulation and experiment results The parameters of the PMSM are taken the same as follows:   Rs = 1.74 Ω, Ld = Lq = 4 mH, ψf = 0.402 Wb,  J = 1.78 × 10−4 kg m2,  B = 7.4 × 10−5 N ms,  np = 4 2017/4/27

Simulation setup Parameter setup The saturation limit of q-axis reference current is 11.78 A. The proportional and integral gains of d-axis current controllers of the two control schemes are kp = 50, ki = 2500. The parameters of q-axis current loop of the speed ESOC scheme are the same as that of the d-axis current loop. The proportional gain and the desired double-pole of ESO of the speed loop of the speed ESOC scheme are k = 1.5, p = 5000. For the current ESOC scheme, the proportional gain and the desired double-pole of the current and speed loops are takes as kq = 50, pq = 2000, and k = 1.5, p = 5000, respectively. The load torque TL = 2.5 Nm is added at t = 0.1 s. 2017/4/27

Simulation results The tracking responses for the q  -axis current loop under speed ESOC and current ESOC methods Fig. 4. Curves of        under speed ESOC and current ESOC methods: (a) the whole curves under speed ESOC method, (b) the whole curves under current ESOC method, 2017/4/27

Simulation results Fig. 4. Curves of        under speed ESOC and current ESOC methods: (c) the local curves of (a) in time domain [0, 0.01] s, (d) the local curves of (b) in time domain [0, 0.004] s, 2017/4/27

Simulation results Fig. 4. Curves of        under speed ESOC and current ESOC methods: (e) the local curves of (a) in time domain [0.099, 0.103] s, and (f) the local curves of (b) in time domain [0.099, 0.103] s 2017/4/27

Simulation results The speed responses of the PMSM system Fig. 5. Response of speed under speed ESOC and current ESOC methods: (a) the whole curves, (b) the local curves in time domain [0, 0.06] s, and (c) the local curves in time domain [0.098, 0.105] s. 2017/4/27

Simulation results Estimation effects of ESO for speed and current loops Fig. 6. The actual and estimate value of disturbances under current ESOC method: (a) a, z2 of speed loop, (b) aq, z12 of q-axis current loop 2017/4/27

Simulation results Estimation effects of ESO for speed and current loops Fig. 6. The actual and estimate value of disturbances under current ESOC method: (c) the local curves of (a) in time domain [0, 0.003] s, (d) the local curves of (b) in time domain [0, 0.008] s, 2017/4/27

Simulation results Estimation effects of ESO for speed and current loops Fig. 6. The actual and estimate value of disturbances under current ESOC method: (e) the local curves of (a) in time domain [0.099, 0.103] s, and (f) the local curves of (b) in time domain [0.099, 0.106] s. 2017/4/27

Experiment setup DSP TMS320F2808 with a clock frequency of 100 MHz An intelligent power module (IPM) with a switching frequency of 10 kHz The Hall-effect devices and are converted through two 12-bit A/D converters An incremental position encoder of 2500 lines 2017/4/27

Experiment setup The saturation limit of q-axis reference current is 11.78 A. The proportional and integral gains of d-axis current controllers of the two control schemes are kp = 42, ki = 2600. The parameters of q-axis current loop of the speed ESOC scheme are the same as that of the d-axis current loop. The proportional gain and the desired double-pole of ESO of the speed loop of the speed ESOC scheme are k = 1.2, p = 330. For the current ESOC scheme, the proportional gain and the desired double-pole of the current and speed loops are takes as kq = 25, pq = 870, and k = 1.2, p = 330, respectively. 2017/4/27

Fig. 8. Response curves of system when the reference speed is 1000 rpm: (a) iq,iq* (b) speed in the absence of load, and (c) speed in the presence of load. 2017/4/27

Fig. 9. Speed response curves when the reference speed is 500 rpm: (a) in the absence of load and (b) in the presence of load. 2017/4/27

Fig. 10. Speed response curves when the reference speed is 1500 rpm: (a) in the absence of load and (b) in the presence of load. 2017/4/27

The performance comparisons 2017/4/27

Conclusion To improve the disturbance rejection ability, a control scheme which employs disturbance rejection control laws for not only speed loop but also the q-axis current loop, has been proposed. Considering the dynamics of q-axis current, the coupling between rotor speed and d-axis current as well as the back electromotive force have been regarded as lumped disturbances for the q-axis current loop. The lumped disturbances have been estimated by using an extended state observer. Thus a composite control law consisting of proportional feedback and feed forward compensation based on disturbance estimation has been developed to control the q-axis current. Simulation and experiment comparisons have been presented to verify the effectiveness of the proposed method. 2017/4/27

References 1. Miklosovic R, Gao ZQ. A robust two-degree-of-freedom control design technique and its practical application. In: 39th IAS annual meeting on industry application conference; 2004. p. 1495–502. 2. Li, Shihua, Cunjian Xia, and Xuan Zhou. "Disturbance rejection control method for permanent magnet synchronous motor speed-regulation system."Mechatronics 22.6 (2012): 706-714. 2017/4/27

Thank you for your attention 2017/4/27